Problem Statement

A fantastic IS is an integer sequence of length $N$ whose every element is between $1$ and $M$ (inclusive) that satisfies the following condition.

• For every integer $i$ such that $1 \le i \le K$, one of the following holds.
• $A_{P_i} < X_i$ and $A_{Q_i} < Y_i$;
  • $A_{P_i} = X_i$ and $A_{Q_i} = Y_i$;
  • $A_{P_i} > X_i$ and $A_{Q_i} > Y_i$.

Determine whether a fantastic IS exists. If it does, find the minimum possible sum of the elements in a fantastic IS.

Constraints

• $1 \le N,M,K \le 2 \times 10^5$
• $1 \le P_i,Q_i \le N$
• $1 \le X_i,Y_i \le M$
• $P_i \neq Q_i$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M K
P_1 X_1 Q_1 Y_1
P_2 X_2 Q_2 Y_2
\vdots
P_K X_K Q_K Y_K

Output

If a fantastic IS exists, print the minimum possible sum of the elements in a fantastic IS; otherwise, print $-1$.